Uncertainty-aware twin support vector machines

Weighted Twin Support Vector Machines with Local Information and its application

KNN weighted reduced universum twin SVM for class imbalance learning

Probabilistic distance based abnormal pattern detection in uncertain series data

A rough margin-based multi-task [formula omitted]-twin support vector machine for pattern classification

Aiming at the sensitivity of twin support vector machines to noise and outliers, an improved fuzzy twin support vector machine is proposed. Aiming at the shortcomings of fuzzy membership based on the distance between a sample and its class center, this algorithm proposes a new fuzzy membership function that can effectively reflect sample uncertainty— based on intra-class hyperplane and sample affinity. When determining the membership function, the intra-class hyperplane replaces the class center, reducing the dependence on the sample set geometry and improving the model generalization ability. At the same time, considering the relation between each sample and the confusion degree of sample points, the sample affinity is applied to the design of membership function, so as to effectively distinguish the effective sample from noise and outliers and improve the classification accuracy. The experimental results show that compared with the twin support vector machine and the classic fuzzy support vector machine, the improved fuzzy twin support vector machine has better classification performance.

Twin support vector machine (TWSVM), which solves classification problems through constructing two nonparallel planes by solving two related SVM-type problems, has become a hot spot in the field of machine learning. In addition to keeping the advantages of SVM, the classification performance of TWSVM is also significantly better than that of SVM. However, there are at least two parameters in TWSVM which need to specify. These parameters make great difference to the classification result of TWSVM and to find the optimal parameters is an important but difficult work. In order to overcome this deficiency, in this paper, we propose the twin support vector machines based on Fruit Fly Optimization Algorithm (FOA-TWSVM). This algorithm uses FOA-TWSVM, which has high optimization ability and small computation complexity, to select the parameters for TWSVM. The experimental results show that this algorithm is able to find the suitable parameters, and has higher classification accuracy compared with some other algorithms.

Possible world based consistency learning model for clustering and classifying uncertain data

Probabilistic range query is a typical problem in the domain of probabilistic database management system. There exist many efforts for supporting such query. However, the state of arts approaches can not efficiently index uncertain data when their probability density function are discrete. In this paper, we propose a general framework to construct summary for uncertain data with any type of PDF. Especially, if the PDF of uncertain data is discrete, we employ a novel machine learning technique named ELM to learn its distribution type and fit the specific function. If this method does not work, we propose a hybrid algorithm to construct its summary. Besides the hybrid summary construction algorithm, we propose a bitwise-based accessing algorithm to speed up the query. Theoretical analysis and extensive experimental results demonstrate the effectiveness of the proposed algorithms.

Twin support vector machines (TWSVM) is based on the idea of proximal SVM based on generalized eigenvalues (GEPSVM), which determines two nonparallel planes by solving two related SVM-type problems, so that its computing cost in the training phase is 1/4 of standard SVM. In addition to keeping the superior characteristics of GEPSVM, the classification performance of TWSVM significantly outperforms that of GEPSVM. However, the stand-alone method requires the solution of two smaller quadratic programming problems. This paper mainly reviews the research progress of TWSVM. Firstly, it analyzes the basic theory and the algorithm thought of TWSVM, then tracking describes the research progress of TWSVM including the learning model and specific applications in recent years, finally points out the research and development prospects.

Discriminative information-based nonparallel support vector machine

Twin support vector machine (TWSVM) is a new machine learning method, as opposed to solving a single quadratic programming problem in support vector machine (SVM), which generates two nonparallel hyperplanes by solving two smaller size quadratic programming problems. However, the TWSVM obtains the final classifier by giving the same importance to all training samples which may be important for classification performance. In order to address this problem, in this paper, we propose a novel entropy-based fuzzy twin bounded support vector machine (EFTBSVM) for binary classification problems. By considering the fuzzy membership value for each sample and assigning it based on the entropy value, the samples with higher class certainty are assigned to relatively larger fuzzy membership. In addition, the proposed EFTBSVM not only maintains the superior characteristics of the TWSVM but also exploits the structural risk minimization principle by introducing a regularization term. The experimental results achieved on synthetic datasets and benchmark datasets illustrate the effectiveness of the proposed method.

The problem of statistical pattern recognition with noisy or imprecise feature measurements is considered. An exact analytical expression is found for the probability of misclassification under this condition, for multiclass multivariate systems. The probability of error exceeds that of the ideal case for the special case of two classes, the a priori conditional probability density functions are assumed to be normal, along with the two cases of feature measurement error, namely normal and uniform probability density functions. Monotonicity of the misclassification probability with measurement error variance is shown. Numerical results are presented for both cases over a workable range of parameters. The study is useful in practical pattern recognition problems.

Support vector machine (SVM), as a supervised learning method, has different kinds of varieties with significant performance. In recent years, more research focused on nonparallel SVM, where twin SVM (TWSVM) is the typical one. In order to reduce the influence of outliers, more robust distance measurements are considered in these methods, but the discriminability of the models is neglected. In this article, we propose robust manifold twin bounded SVM (RMTBSVM), which considers both robustness and discriminability. Specifically, a novel norm, that is, capped L₁-norm, is used as the distance metric for robustness, and a robust manifold regularization is added to further improve the robustness and classification performance. In addition, we also use the kernel method to extend the proposed RMTBSVM for nonlinear classification. We introduce the optimization problems of the proposed model. Subsequently, effective algorithms for both linear and nonlinear cases are proposed and proved to be convergent. Moreover, the experiments are conducted to verify the effectiveness of our model. Compared with other methods under the SVM framework, the proposed RMTBSVM shows better classification accuracy and robustness.

Support vector machine (SVM) has a good effect in the supervised classification of hyperspectral images. In view of the shortcomings of the existing parallel structure SVM, this article proposes a non-parallel SVM model. Based on the traditional parallel boundary structure vector machine, this model adds an additional empirical risk minimization term to the original optimization problem by adding the least square term of the sample and obtains two non-parallel hyperplanes, respectively, forming a new non-parallel SVM algorithm to minimize the additional empirical risk of non-parallel SVM (Additional Empirical Risk Minimization Non-parallel Support Vector Machine, AERM-NPSVM). On the basis of AERM-NPSVM, the bias constraint is added to it, and AERM-NPSVM (BC-AERM-NPSVM) is further obtained. The experimental results show that, compared with the traditional parallel SVM model and the classical non-parallel SVM model, Twin Support Vector Machine (TWSVM), the new model, has a better effect in hyperspectral image classification and better generalization performance.

In this study, banks’ business performance efficiency was analysed using data envelopment analysis (DEA), with expense categories as inputs and income categories as outputs. By incorporating a bootstrap method and a fuzzy data approach into a DEA model, additional insights and sensitivity analysis of the results were obtained. This study shows how fuzzy and bootstrap DEA can be used for investigating real market problems with uncertain data in an uncertain sample. The empirical analysis was based on the period of 2009–2018 for a sample of seven of Croatia’s largest private banks. The aim of the study was also to interpret the DEA results with regards to the specific market, legal, and macroeconomic conditions, caused by the changes introduced in the last decade. The results, and the changes in the inputs and outputs over time, revealed that the market processes occurring in the observed period had a significant impact on banks’ business performance, but led to a more efficient banking system. Two banks were found to be dominant over the others regardless of the changes in the sample and data fuzziness. DEA results were additionally compared to the most important financial indicators and accounting ratios, as an alternative or additional measure of banks’ efficiency and profitability.